What are the divisors of 536?

1, 2, 4, 8, 67, 134, 268, 536

There is a total of 8 positive divisors.
The sum of these divisors is 1020.
The arithmetic mean is 127.5.

6 even divisors

2, 4, 8, 134, 268, 536

2 odd divisors

1, 67

How to compute the divisors of 536?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 536 by each of the numbers from 1 to 536 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

536 / 1 = 536 (the remainder is 0, so 1 is a divisor of 536)
536 / 2 = 268 (the remainder is 0, so 2 is a divisor of 536)
536 / 3 = 178.66666666667 (the remainder is 2, so 3 is not a divisor of 536)
...
536 / 535 = 1.0018691588785 (the remainder is 1, so 535 is not a divisor of 536)
536 / 536 = 1 (the remainder is 0, so 536 is a divisor of 536)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 536 (i.e. 23.15167380558). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

536 / 1 = 536 (the remainder is 0, so 1 and 536 are divisors of 536)
536 / 2 = 268 (the remainder is 0, so 2 and 268 are divisors of 536)
536 / 3 = 178.66666666667 (the remainder is 2, so 3 is not a divisor of 536)
...
536 / 22 = 24.363636363636 (the remainder is 8, so 22 is not a divisor of 536)
536 / 23 = 23.304347826087 (the remainder is 7, so 23 is not a divisor of 536)